Compressed sensing phase retrieval with phase diversity

The compressed sensing (CS) theory shows that sparse signal can be reconstructed accurately with some randomly observed measurements that are much fewer than what traditional method requires. Since it takes structure of signals into consideration, it has many advantages in the structured signals process. With CS, measuring can be speeded up and the cost of hardware can be decreased significantly. However, it faces great challenge in the amplitude-only measurement. In this article, we study the magnitude-only compressed sensing phase retrieval (CSPR) problem, and propose a practical recovery algorithm. In our algorithm, we introduce the powerful Hybrid-Input–Output algorithm with phase diversity to make our algorithm robust and efficient. A relaxed ℓ0ℓ0 norm constrain is also introduced to help PR find a sparse solution with fewer measurements, which is demonstrated to be essential and effective to CSPR. We finally successfully apply it into complex-valued object recovery in THz imaging. The numerical results show that the proposed algorithm can recover the object pretty well with fewer measurements than what PR traditionally requires.